Applicability of the Newtonian gap-bound approach to heat currents

Determine whether the derivation of universal upper bounds on the energy gap in topological systems, based on Newton’s laws/Ehrenfest theorem and bulk electrical or spin transport, extends to quantized heat transport in topological matter, given that the method assumes bulk current flow while low-temperature heat currents in gapped phases propagate along edge modes rather than through the bulk.

Background

The paper provides a simpler, physically intuitive derivation of a universal upper bound on the energy gap in topological systems, originally discovered by Onishi and Fu, and generalizes it to anisotropic systems, three-dimensional insulators, multiple carrier types, and spin Hall systems. The approach relies on Newton’s laws (via the Ehrenfest theorem), canonical commutation relations, and bulk response to uniform electric fields.

While the method successfully treats charge and spin transport in the bulk, thermal transport in gapped topological phases occurs via edge modes. This difference raises a specific uncertainty about whether the bulk-based derivation can be adapted to heat currents, motivating an explicit open problem regarding the extension of the approach to quantized thermal transport.